If a rational number can be found between any two irrationals, and the set of
irrationals are uncountably infinite, does that mean that the rationals are also
uncountable? Doctor Peterson points up the flaw in a student's assumption about what
to conclude from a failed mapping.

I am having difficulty understanding 'vacuous' situations such as if A
is an empty set and B is a non-empty set, then why is there one
function mapping A to B (the empty function) but no function mapping B
to A?

The science club advisor asked club members what science courses they
liked. Eighteen members said they liked physics, 17 liked chemistry,
and 10 liked biology. However, of these, 9 liked physics and
chemistry, 4 liked biology and chemistry, 2 liked physics and biology,
and 2 liked all three. How many science club members were interviewed?

At a fork in a road are identical twins. One always lies and one always
tells the truth, but you don't know which is which. If you could only ask
one question to find out which way to go, what would it be?